1640s, "to disable, render useless," a figurative verbal extension from the noun hamstring "tendon at the back of the knee" (1560s), from ham "bend of the knee" (see ham (n.1)) + string. Cutting this would render a person or animal lame. Related: Hamstrung.

[I]n hamstring, -string is not the verb string; we do not string the ham, but do something to the tendon called the hamstring; the verb, that is, is made not from the two words ham & string, but from the noun hamstring. It must therefore make hamstringed. [Fowler]

(hām'strĭng') A powerful group of muscles at the back of the thigh that arise in the hip and pelvis and insert as strong tendons behind the knee. The hamstring bends the knee and helps to straighten the hip.